Based on OP's comment that deseasonalized time series is a linear trend (t is a true predictor), then you will either want the Prediction Interval for linear regression (if you are trying to predict 1 time period ahead), or tolerance intervals if you are trying to capture a specific proportion of future measurements.

If the residuals from your linear fit to the deseasonalized data are approximately normal, then there are nice formulas for as you will see in the above links: Also, eee this other CrossValidated Post.

You would then re-seasonalize these intervals/bands to get your actual forcasts.

Based on OP's comment that deseasonalized time series is a linear trend (t is a true predictor), then you will either want the Prediction Interval for linear regression (if you are trying to predict 1 time period ahead), or tolerance intervals if you are trying to capture a specific proportion of future measurements.

If the residuals from your linear fit to the deseasonalized data are approximately normal, then there are nice formulas for as you will see in the above links: Also, eee this other CrossValidated Post.

You would then re-seasonalize these intervals/bands to get your actual forcasts.